M=7 (1,3) runlength limited code for multi-level data

ABSTRACT

A system for encoding digital data with an M-ary (d,k) code to provide multi-level coded data where M&gt;2 comprises an M-ary (d,k) encoder for accepting digital input data. The M-ary (d,k) coder encodes the digital input data to produce a plurality of code symbols, where each code symbol is at one of M levels and each pair of non-zero code symbols is separated by at least d but no more than k zeros. A waveform encoder converts the code symbols into waveform signal amplitudes compatible with a multi-level channel. Each waveform signal amplitude is generated by modulo M addition of a current code symbol with a previous waveform signal amplitude. A specific M=7 (1,3) code provides high density recording to a multi-level storage medium. The M=7 (1,3) encoder is implemented using a three-state encoder and a modulo seven waveform encoder.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to multi-level coding techniques, and more specifically to a system and method for coding data using an M=7 (1,3) runlength limited code, such code being particularly useful for storing and/or transmitting multi-level data.

2. Related Art

Various techniques are currently in use for increasing the recording density on various digital recording mediums such as magnetic tapes and disks and in other similar media. One technique utilizes an approach known as run-length-limited coding. This technique requires that each "1" in a coded bit sequence must be separated by a specified number of "0's". This number of zeros must be at least a minimum quantity, d, to reduce intersymbol interference, and is limited to a maximum quantity k for self clocking purposes. Such codes are generally referred to as (d,k) run-length-limited (RLL) codes.

Because conventional recording techniques use saturation recording to store information, binary recording techniques are often used to mark the recording medium. As a result, conventional (d,k) RLL codes developed to date are developed and optimized to store binary data.

Significant advances in data storage materials have lead to the development of a storage medium that provides a linear response characteristic. One such material providing a linear response characteristic is an electron trapping material such as is disclosed in U.S. Pat. Nos. 4,864,536, 5,007,037, and 5,142,493, all to Lindmayer.

Using a material which provides a linear response characteristic yields an advantage over saturation-type media in that it adds an analog dimension to the storage capacity of the medium. Because the response is linear, the linear-response storage materials provide the ability to encode information in two dimensions--amplitude and phase.

As a result, the storage medium is no longer confined to storing binary or even tri-level data. Instead, the concept of M-ary, or non-binary, data coding and storage is provided. The increased symbol set allowed by such encoding provides the opportunity to dramatically increase the data recording density and transfer rate of the storage device. For example, the potential storage capacity of a single 51/4 inch disk can be extended to several gigabytes if that disk is implemented using electron trapping materials with M-ary (multi-level) data coding.

SUMMARY OF THE INVENTION

The present invention is directed toward an M=7 (1,3) runlength-limited code for multi-level data storage and/or communications. Also disclosed herein is a system and method for generating multi-level data from a binary input data stream using an M-ary (d,k) code such as the M=7 (1,3) runlength limited code.

According to the invention input data bits are coded using an M-ary (d,k) encoder to generate code symbols. Specifically, input data bits x are encoded using the M-ary (d,k) encoder to generate code symbols y, where:

x=(x₀, x₁, . . . x_(p-1)), for p input data bits

y=(y₀, y₁, . . . y_(q-1)), where p/q=the code rate R

The code symbols y are multi-level symbols, each being at one of M levels. The code symbol stream provided meets the code specifications of no fewer than d and no greater than k zeros between each non-zero symbol. Thus, according to the M=7 (1,3) code disclosed herein, code symbols are each at one of seven levels and there is a minimum of one and a maximum of three zeros between each non-zero symbol.

The code symbols y are encoded to generate a series of waveform amplitudes z. The waveform amplitudes are generated by modulo M addition of the current code symbol Y_(i) with the previous waveform amplitude z_(i-1). The waveform amplitudes are used to modulate a write laser to store information onto an optical disk or to otherwise store or communicate the input data bits x in the form of multi-level information.

To recover the original data bits x from the medium, the information stored on the medium is read and the resultant signal amplitudes are decoded. Two stages of decoding are provided. In the first stage, the waveform amplitudes are decoded to generate code symbols. In the second stage, the code symbols are decoded to recover the original data bits.

The system and method described herein for coding and decoding the data is described with respect to the M=7 (1,3) code disclosed herein. However, while other codes may not be obvious in light of the code disclosed herein, given a specific M-ary (d,k) code, after reading the below disclosure, it will become apparent to a person skilled in the relevant art how the disclosed system and method can be implemented to code and decode the data using such a specific M-ary (d,k) code.

An advantage of the invention is that the recording density can be increased by coding the input data using the disclosed M=7 (1,3) code. Because there are at least d zeros between every non-zero code symbol, there can be at least d+1 symbols stored for a given minimum feature size. Given a code of rate R, the density achievable is (d+1)R.

It should be noted that the coding techniques described herein are not limited to optical recording. Other recording systems capable of supporting multi-level data would benefit from the coding techniques described herein. Additionally, these coding techniques are also applicable to communications systems where the communications channel is capable of supporting multi-level data. In such an implementation, the waveform amplitudes could be used to modulate a signal carrier for transmission across the multi-level channel.

Further features and advantages of the present invention, as well as the structure and operation of various embodiments of the present invention, are described in detail below with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described with reference to the accompanying drawings. In the drawings, like reference numbers indicate identical or functionally similar elements. Additionally, the left-most digit(s) of a reference number identifies the drawing in which the reference number first appears.

FIG. 1 is a diagram illustrating a portion of an optical storage medium and features thereon.

FIG. 2 is a diagram illustrating a data storage system for storing a multi-level coded data.

FIG. 3 is a diagram illustrating an encoder for encoding multi-level data using a multi-level (d,k) code.

FIG. 4 is a flow diagram illustrating the operation of a multi-state encoder.

FIG. 5 is a diagram illustrating an example input data stream being coded using the encoder illustrated in FIG. 4.

FIG. 6 is a diagram illustrating a decoder for decoding multi-level (d,k) coded data.

FIG. 7 is a diagram illustrating a sliding block decoder.

DETAILED DESCRIPTION OF THE EMBODIMENTS

1. Introduction

The present invention is directed toward an M-ary (d,k) code for use in storage and/or transmission of multi-level data, and a system and method for generating the same. This discussion is provided in several sections. In Section 2, before discussing the invention in detail, a brief discussion of binary (d,k) codes is presented. In Section 3, a coding system for coding input data using an M-ary (d,k) code is described. In Section 4, some code design factors are described. In Section 5, a specific M=7 (1,3) code is described that is particularly useful for storage and/or transmission of multi-level data. Section 5 also provides a detailed description of the encoder used to code data using the disclosed M=7 (1,3) code. In Section 6 there is presented a discussion of a sliding block decoder generally useful for decoding M-ary (d,k) codes, as well as a specific decoder for decoding the M=7 (1,3) code described in Section 4.

The present invention is generally described in terms of an embodiment where multi-level data are stored on and retrieved from an optical disk. In such an embodiment, the encoder and decoder described herein may be implemented for multi-level data storage in an optical disk system such as that disclosed in U.S. Pat. No. 5,007,037, which is incorporated herein by reference. However, after reading the below description, it will become apparent to a person skilled in the relevant art how the systems and methods of the invention can be implemented for alternative applications such as multi-level data communications and storage of multi-level data on media other than optical disks. In yet other alternative embodiments, the invention can be implemented to transmit and receive data across an M-ary communications channel. In this document, the term "channel" is sometimes used to refer to the optical disk. It should be understood that in the alternative embodiments the term channel can be used to describe alternative storage media and/or communications channels.

Additionally, after reading the below detailed description of the encoder and decoder of the present invention, it will become apparent to a person skilled in the art that these disclosed components can be implemented using hardware, software or a combination of both hardware and software.

2. Binary (d,k) Run-Length-Limited Coding

Using conventional binary storage techniques, data are written to a storage medium using binary 1's and 0's. Using run-length limited coding, the data to be recorded are first encoded using a run-length-limited encoder. As stated above, with a (d,k) RLL code, there is a minimum and a maximum number of 0's that can occur between each pair of 1's, as specified by the code parameters d and k. Thus, the (d,k) RLL encoder results in a 1 followed by at least d and at most k 0's before another 1 occurs. Such (d,k) RLL codes for binary applications are well known in the art.

To write input data to the saturation storage medium, the input data are first encoded to create symbols. The encoder is designed such that the output symbols conform to the code specifications: each 1 is followed by a minimum of d and a maximum of k 0's. These symbols are then written to the storage medium as a series of features. For example, for optical disks, a feature is the presence or absence of a burn mark. In a magnetic tape, the feature is a grouping of magnetic particles oriented in a particular manner.

FIG. 1 illustrates a portion of an optical storage medium 108 that stores binary data as features 102. Illustrated are shaded and unshaded features 102, indicating the absence or presence of a burn mark. Also illustrated in FIG. 1 is an example symbol stream 112 that is used to write the features 102 to medium 108. As discussed above, symbol stream 112 is the result of encoding input data using a (d,k) RLL code. Symbol stream 112 is written to medium 108 using an additional coding step as follows: the occurrence of a 1 indicates a change in the type of mark (i.e., absence or presence of a burn mark); the occurrence of a 0 indicates no change in mark type. This additional coding step is sometimes referred to as non-return-to-zero interleaved (NRZI) precoding.

Note that with a (d,k) RLL code where d=2, the minimum number of symbols represented by a single feature 102 is three. Thus, for a minimum feature size (e.g., for the smallest spot size on medium 108) three symbols can be represented. As a result, for a rate 1/2 code, where each input bit corresponds to two symbols, the minimum density of data written to medium 108 is 1.5 bits per feature. Thus, as a result of using the (d,k) RLL coding in the described scenario, the density of the recording system can be increased by 50%.

3. A Generic M-ary Runlength-Limited (d,k) Coder

A few advantages of (d,k) coding are described above with reference to binary data systems. It is important to note that similar gains in density can be realized for storage and communications systems using multi-level (versus binary) data. To optimize such gains, however, new codes and new coding techniques are required to take full advantage of the unique properties of the multi-level data. Thus, the inventors have developed a system and method for encoding data using M-ary (d,k) codes.

FIG. 2 is a high-level block diagram generally illustrating a multi-level data recording system 200. The recording system is comprised of an encoder 204, multi-level storage medium 208 and a decoder 212. As stated above, multi-level storage medium 208 can be replaced with a communications channel allowing the multi-level (d,k) code and coding scheme to be used with multi-level data communications. In such a communications embodiment, encoder 204 and decoder 212 can be provided on both ends of the communications channel to allow bi-directional coded communications.

According to the invention, input data bits x=(x₀, x₁, . . . , x_(p-1)) are the actual data that a user wishes to be stored on and retrieved from medium 208. However, to take full advantage of the multi-level properties of medium 208 and to increase the storage density achieved, the invention provides for the encoding of input data x so that multi-level data is stored on medium 208. Such encoding is accomplished using encoder 204.

In one embodiment, encoder 204 is implemented as a two-stage encoder. FIG. 3 is a block diagram illustrating encoder 204 in this embodiment. Referring to FIG. 3, encoder 204 is comprised of a symbol encoder 304 and a waveform encoder 308, referred to herein as encoder 304 and encoder 308, respectively.

Encoder 304 is a (d,k) RLL symbol encoder that accepts the input data bits x and converts them to a stream of code symbols y=(Y₀, Y₁, . . . , Y_(q-1)). To take advantage of the multi-level characteristics of medium 208, encoder 304 generates code symbols y at M different levels, where M>2. A second feature of encoder 304 is that the stream of code symbols y meets the code specification that there are no fewer than d and no greater than k zeros between each non-zero code symbol. Another feature of encoder 304 is that there are R input bits x_(i) for each code symbol Y_(i) generated. This feature is referred to as the code rate. Thus for a rate 1/N code (i.e., where R=1/N), there are N code symbols y_(i) generated for each input data bit x_(i).

Waveform encoder 308 accepts Code symbols y and converts them to a series of waveforms z=(z₀, z₁, . . . , z_(q-1)), each of a given amplitude. Waveform encoder 308 generates output waveforms z, each at one of M different amplitudes. The waveform amplitudes are generated by modulo M addition of the current code symbol y_(i) with the previous waveform amplitude z_(i-1). It is the waveforms z which are used to modulate a write laser for storing data onto medium 208 (or transmitted across the multi-amplitude channel).

Because there are at a minimum d zeros, between each non-zero code symbol, each waveform amplitude z generated represents, at a minimum, d+1 code symbols y. Also, because there are 1/R code symbols y generated for each input data bit x, each waveform amplitude z generated represents, at a minimum, (d+1)R data bits x. Thus, for a minimum feature size (e.g., the smallest spot that can be written to the storage medium or the shortest pulse that can be transmitted across the communications channel), the density achieved is D=(d+1)R.

Consider this density in terms of the specific M=7 (1,3) code described below. The rate of this code is R=3/2 and d=1. For this code, the density is 3.0 input data bits x_(i) per minimum feature size. In other words, 3.0 input data bits can be stored using a single minimum-size feature.

4. Code Design Factors

The coding system and method described above can be used to code input data using any of number of M-ary (d,k) codes. However, the design of a specific M-ary (d,k) code is not a trivial matter.

There are several factors that must be taken into consideration when designing M-ary (d,k) codes. The specific coding scheme used to implement a given code impacts the performance of the encoding and decoding systems. For example, the code should be designed such that encoders and decoders can be implemented in a straight-forward and cost-effective manner. Toward this end, the desirable code can be implemented using encoders that have a relatively small number of states while still meeting the code parameters (i.e., M, d and k). Additionally, the decoder required to decode the coded data should be implementable using a small sliding block window size and the decoder should have a relatively a small table size.

Further, the code design must result in an encoder and decoder that operate such that errors in the decoder side have a minimum effect. It would be undesirable for errors to propagate too far in the decoded data stream. In some less-than-desirable systems, a single decoding error can result in a very large, if not infinite, number of additional decoding errors.

Achievement of such design goals is not a trivial matter. Not every M-ary (d,k) code of a given set of parameter values will perform in a desirable manner. Provided in the next section of this document is a specific M=7 (1,3) runlength-limited code that meets the design goals outlined above.

5. M=7 (1,3) runlength-limited code

As stated above, code design is not a trivial matter as there are several coding factors that affect the performance of the system. The specific code implemented for a given set of parameters can impact the overall performance of the system. This section of the patent document describes a specific M-ary (d,k) code and the specific encoder used to implement this code. In particular, this section describes a specific M=7 (1,3) runlength-limited code having a rate R=3/2.

Table 1 is a state table illustrating a state machine 400 for encoding input data x to generate code symbols y for the M=7 (1,3) code (i.e. a specific version of encoder 304). State machine 400 is a three-state, M=7 (1,3) encoder. For each input data bit set x_(i) . . . x_(i+2), an output code symbol set Y_(i), Y_(i+1) is produced; each output code symbol y_(i) is at one of seven levels (0-6). The various states as well as the inputs and outputs of state machine 400 are illustrated using Table 1.

FIG. 4 is an operational flow diagram illustrating the operation of state machine 400. The operation of state machine 400 is now described with reference to Table 1 and FIG. 4. In a step 404, the operation starts in a given state at time t=0. In a step 408, an input data bit set x_(i) . . . x_(i+2) is received. In a step 412, Table 1 is used to determine the output code symbol set Y_(i), Y_(i+1) and next state from the current state and the input data bit set x_(i) . . . x_(i+2) received in step 408. In a step 416, encoder 304 outputs code symbol set y_(i), y_(i+1) determined in step 412. In a step 420, state machine 400 transitions to the next state determined in step 412. At this time, the operation continues at step 408 as indicated by flow line 426.

As is evident by the above description, an output code symbol set y_(i), y_(i+1) of encoder 304 is a function of the input data bit set x_(i) . . . x_(i+2), and the current state 404 of encoder 304. For the M=7 (1,3) encoder of the present invention, Table 1 describes the output code symbol set y_(i), y_(i+1) and next state of encoder 304 for each current state and input data bit set x_(i) . . . x_(i+2).

                  TABLE 1                                                          ______________________________________                                         INPUT         OUTPUT   NEXT STATE                                              ______________________________________                                         STATE 0                                                                        000           01       0                                                       001           02       0                                                       010           03       0                                                       011           04       0                                                       100           05       0                                                       101           06       0                                                       110           00       1                                                       111           00       2                                                       STATE 1                                                                        000           01       0                                                       001           02       0                                                       010           03       0                                                       011           04       0                                                       100           05       0                                                       101           06       0                                                       110           20       1                                                       111           20       2                                                       STATE 2                                                                        000           30       1                                                       001           30       2                                                       010           40       1                                                       011           40       2                                                       100           50       1                                                       101           50       2                                                       110           60       1                                                       111           60       2                                                       ______________________________________                                    

To further illustrate the operation of symbol encoder 304, consider an example input data stream x as illustrated in Table 2. In this example, assume the encoder 304 starts in state 0 and that the first input data bit set x_(i) . . . x_(i+2) is `101`. Referring to Table 1 for state 0, the row where x_(i) . . . x_(i+2) =`101` indicates that encoder 304 outputs symbol `06` and transitions to state 0.

FIG. 5 is a diagram further illustrating the example. FIG. 5 illustrates a current state 508 and a new state 512 for the example input data stream provided in Table 2. Referring to FIG. 5 and state machine 400, given the input data stream illustrated in Table 2, for each input data bit set x_(i) . . . x_(i+2), encoder 304 transitions from a current state 508 to a new state 512 and produces an output symbol set y_(i), y_(i+1). FIG. 5 illustrates the example for 15 data bits x of the input data stream while Table 2 is an example for 15 data bits x.

                  TABLE 2                                                          ______________________________________                                         x   1  0  1   1  0  1  1  0  1  0  1  0                                                                               1  0  0                                 y   06        06       06       03     05                                      z   06        64       42       25     52                                      ______________________________________                                    

As described above with reference to FIG. 3, code symbols y are further coded by waveform encoder 308 to generate a sequence of amplitudes z used to modulate the write laser. According to one embodiment, waveform encoder 308 is a modulo seven encoder that, for a given time, determines the waveform amplitude z_(i) by

    z.sub.i =(z.sub.i-1 +y.sub.i)mod M

Note that z is a transformed version of y, where the difference (mod M) between waveform amplitudes z_(i) and z_(i-1) is the coded symbol y_(i). Thus, in this embodiment, each new code symbol y_(i) is modulo seven added to the previous waveform amplitude z_(i-1) to result in the current waveform amplitude z_(i). In following the example described above and illustrated in FIG. 5 and Table 2, the code symbols y are encoded by waveform encoder 308 to waveform amplitudes z, as illustrated in Table 2.

To briefly summarize the encoding process, input digital data bits x are first encoded using an M=7 (1,3) symbol encoder to produce code symbols y at M=7 levels. Code symbols y are then encoded by waveform encoder 308 to produce waveform amplitudes z. According to the current code, M=7 amplitudes (illustrated in the above examples as 0-6) are possible. These amplitudes are written to the media by the write laser as illustrated in FIG. 3.

6. Decoder

In order to recover the original data bits x from the amplitudes z stored on the media (or transmitted across the communications channel) a decoder is implemented. In one embodiment, the decoder uses a state independent lookup table to decode amplitude levels z read from the disk. In this embodiment, the decoder is a sliding block decoder, where a sliding window is used to decode amplitudes read from the disk.

FIG. 6 is a block diagram illustrating the decoder. As illustrated in FIG. 6, decoder 212 is comprised of a waveform decoder 604 and a sliding block decoder 608. Waveform decoder 604 receives the signal amplitudes z' (multi-level) from the media and converts them to a sequence of digital code Symbols y'. Sliding block decoder 608 performs a table lookup to convert output code symbols y' into output data bits x'. Note that in an error free environment, output code symbols y' correspond identically to input code symbols y and output data bits x' correspond identically to input data bits x.

Any of a number of different techniques can be implemented to read waveform amplitudes z off of the media to provide the signal amplitudes z' to waveform decoder 604. It should be noted that the actual read scheme implemented is not important to the invention as long as data are read accurately.

As stated above, the purpose of waveform decoder 604 is to decode signal amplitudes z' to recover the actual code symbols y'. Waveform decoder converts a sequence of amplitudes z'=(z'₀, z'₁, . . . , z'_(N-1)) where z'_(i) ε[0,A], for some real number A, to a sequence of code symbols y'=(Y'₀, Y'₁, . . . , Y'_(N-1).

The operation of waveform decoder 604 is now described. For a given time i, the code symbol Y'_(i) is determined by

    y'.sub.i =(z'.sub.i -z'.sub.i-1)mod M

According to this technique, each output symbol y' is determined as being the modulo M difference between the current amplitude waveform z'_(i) and the previous amplitude waveform z'_(i-1). This decoding essentially undoes the coding performed by waveform encoder 308. Specifically, for M=7 (d,k) codes, such as the M=7 (1,3) code described above in Section 5, the decoding is implemented using a modulo seven difference.

6.1 Sliding Block Decoder

The purpose of sliding block decoder 608 is to convert the sequence of code symbols y' into a sequence of data bits x' that coincide with input data bits x. In a preferred embodiment, the decoder is a state independent lookup table. The size of the lookup table is dependent on the specific code implemented. Therefore, the design of encoder 304 affects the size of the lookup table implemented.

Sliding block decoder 608 is illustrated in FIG. 7. Sliding block decoder comprises a sliding window 704 to decode the code symbols y' to arrive at output data bits x'. Whereas encoder 304 accepts one data bit set x_(i) . . . x_(i+2) and generates one code symbol set Y_(i), Y_(i+1) therefrom, sliding block decoder 608 must look at multiple code symbols y' to decode one data bit set. Specifically, for the encoder described above with reference to Table 1, sliding block decoder 608 requires a block of six code symbols y_(i) ' to uniquely decode one data bit set x_(i) '. . . x_(i+2) '.

The actual size of sliding window 704 is determined during code design. An optimally sized sliding window 704 is large enough such that the symbols y' within sliding window 704 unambiguously define the correct output bit set x' without being so large that unneeded code symbols y' are included therein. In other words, the window size is chosen as the smallest window which guarantees unique decodability.

With the use of a sliding window 704 to decode the data, knowledge of state information is not required. In fact, the contents of sliding window 704 at any given time contain sufficient information such that state information can be determined therefrom. Thus, sliding block decoder 608 is computationally less complex than conventional decoders; more importantly, the sliding block decoder limits the propagation of errors.

Sliding window 704 actually represents the past, present and future. The code symbols y' actually being decoded to generate data bits x' represent the present. Past symbols y' are those occurring earlier in time than the present symbols. Likewise, future symbols y' are those that occur after the present symbols. In FIG. 7, the past is represented by `06`, the present by `06`, and the future by `03`.

Note that sliding block decoders are well known for decoding binary data. One well known technique for implementing sliding block decoders with binary data is the Adler-Coppersmith-Hassner technique disclosed in U.S. Pat. No. 4,413,251. Another, related technique is disclosed in U.S. Pat. No. 4,882,583 to Dimitri et al. According to these techniques, the number of past symbols required in the window is fixed based on the code design. The number of future symbols should be maintained as small as possible. These goals apply to the M-ary sliding block decoder as well.

The lookup table contains a plurality of entries. In one embodiment, each entry contains a possible sequence of N code symbols y', where N is the size of sliding window 704. In alternative embodiments, each entry of the lookup table is addressed by (directly, indirectly or via a decoding scheme) one of the possible sequences of code symbols.

Based on the specific design of coder 304, there are a limited number of possible occurrences of N code symbols y'. The lookup table comprises a sufficient number of entries such that there is one entry for each of the possible occurrences of N code symbols. As stated above, N is chosen such that for each sequence of N code symbols y' an output bit set x' is unambiguously defined.

For the encoder 304 described above with reference to Table 1, the preferred lookup table has 900 entries and is illustrated in Table 3. For each entry of six code symbols y', there is an output bit set x'. Thus, to decode code symbols y', six consecutive code symbols y' are loaded into sliding window 704. The entry corresponding to those six code symbols y' is located in the lookup table and the corresponding data bit set x' is output. To determine the next output data bit set x', sliding window 704 is `slid` one code symbol set y' into the future (i.e., in one embodiment, a next code symbol set y' is shifted into window 704 and the oldest shifted out) and the lookup process is repeated. This sliding process continues as long as code symbols y' are provided to sliding block decoder 608.

In one embodiment, the contents of window 704 are real-valued and, therefore, the table entry retrieved is the entry that is closest in squared Euclidean distance. Specifically, for a given window w=(w₁, . . . , w₆), the distance d_(j) for each table entry t_(j) is computed as: ##EQU1## where, t_(ji) is the i'th component of the j'th table entry. The window w is then decoded to the table entry with the minimum distance d_(j).

Other embodiments are contemplated where the contents of window 704 are used as an address or used to generate an address of an entry in a memory, where the contents of that entry contain the appropriate output data bit set x'.

The complexity of the decoding process can be reduced significantly by making hard decisions regarding read signal amplitudes. Specifically, in one embodiment, the read signal amplitudes z' are rounded-off or quantized to be one of the seven permissible amplitude levels. Even though this results in a decrease in the performace of the decoder it can significantly reduce its complexity: that is, the table can be a true lookup table requiring no distance calculations.

It should be noted that at the beginning and the end of a data stream, there is a period of time during which window 704 is not full.

                                      TABLE 3                                      __________________________________________________________________________     Sequence of                                                                               Sequence of                                                                              Sequence of                                                                              Sequence of                                                                              Sequence of                           Code       Code      Code      Code      Code                                  Symbols                                                                               x'  Symbols                                                                               x' Symbols                                                                               x' Symbols                                                                               x' Symbols                                                                               x'                             __________________________________________________________________________     010101 000 020100 000                                                                               030206 001                                                                               040305 010                                                                               050404 011                            010102 000 020201 001                                                                               030200 001                                                                               040306 010                                                                               050405 011                            010103 000 020202 001                                                                               030301 010                                                                               040300 010                                                                               050406 011                            010104 000 020203 001                                                                               030302 010                                                                               040401 011                                                                               050400 011                            010105 000 020204 001                                                                               030303 010                                                                               040402 011                                                                               050501 100                            010106 000 020205 001                                                                               030304 010                                                                               040403 011                                                                               050502 100                            010100 000 020206 001                                                                               030305 010                                                                               040404 011                                                                               050503 100                            010201 001 020200 001                                                                               030306 010                                                                               040405 011                                                                               050504 100                            010202 001 020301 010                                                                               030300 010                                                                               040406 011                                                                               050505 100                            010203 001 020302 010                                                                               030401 011                                                                               040400 011                                                                               050506 100                            010204 001 020303 010                                                                               030402 011                                                                               040501 100                                                                               050500 100                            010205 001 020304 010                                                                               030403 011                                                                               040502 100                                                                               050601 101                            010206 001 020305 010                                                                               030404 011                                                                               040503 100                                                                               050602 101                            010200 001 020306 010                                                                               030405 011                                                                               040504 100                                                                               050603 101                            010301 010 020300 010                                                                               030406 011                                                                               040505 100                                                                               050604 101                            010302 010 020401 011                                                                               030400 011                                                                               040506 100                                                                               050605 101                            010303 010 020402 011                                                                               030501 100                                                                               040500 100                                                                               050606 101                            010304 010 020403 011                                                                               030502 100                                                                               040601 101                                                                               050600 101                            010305 010 020404 011                                                                               030503 100                                                                               040602 101                                                                               050001 110                            010306 010 020405 011                                                                               030504 100                                                                               040603 101                                                                               050002 110                            010300 010 020406 011                                                                               030505 100                                                                               040604 101                                                                               050003 110                            010401 011 020400 011                                                                               030506 100                                                                               040605 101                                                                               050004 110                            010402 011 020501 100                                                                               030500 100                                                                               040606 101                                                                               050005 110                            010403 011 020502 100                                                                               030601 101                                                                               040600 101                                                                               050006 110                            010404 011 020503 100                                                                               030602 101                                                                               040001 110                                                                               050020 110                            010405 011 020504 100                                                                               030603 101                                                                               040002 110                                                                               050030 111                            010406 011 020505 100                                                                               030604 101                                                                               040003 110                                                                               050040 111                            010400 011 020506 100                                                                               030605 101                                                                               040004 110                                                                               050050 111                            010501 100 020500 100                                                                               030606 101                                                                               040005 110                                                                               050060 111                            010502 100 020601 101                                                                               030600 101                                                                               040006 110                                                                               060101 000                            010503 100 020602 101                                                                               030001 110                                                                               040020 110                                                                               060102 000                            010504 100 020603 101                                                                               030002 110                                                                               040030 111                                                                               060103 000                            010505 100 020604 101                                                                               030003 110                                                                               040040 111                                                                               060104 000                            010506 100 020605 101                                                                               030004 110                                                                               040050 111                                                                               060105 000                            010500 100 020606 101                                                                               030005 110                                                                               040060 111                                                                               060106 000                            010601 101 020600 101                                                                               030006 110                                                                               050101 000                                                                               060100 000                            010602 101 020001 110                                                                               030020 110                                                                               050102 000                                                                               060201 001                            010603 101 020002 110                                                                               030030 111                                                                               050103 000                                                                               060202 001                            010604 101 020003 110                                                                               030040 111                                                                               050104 000                                                                               060203 001                            010605 101 020004 110                                                                               030050 111                                                                               050105 000                                                                               060204 001                            010606 101 020005 110                                                                               030060 111                                                                               050106 000                                                                               060205 001                            010600 101 020006 110                                                                               040101 000                                                                               050100 000                                                                               060206 001                            010001 110 020020 110                                                                               040102 000                                                                               050201 001                                                                               060200 001                            010002 110 020030 111                                                                               040103 000                                                                               050202 001                                                                               060301 010                            010003 110 020040 111                                                                               040104 000                                                                               050203 001                                                                               060302 010                            010004 110 020050 111                                                                               040105 000                                                                               050204 001                                                                               060303 010                            010005 110 020060 111                                                                               040106 000                                                                               050205 001                                                                               060304 010                            010006 110 030101 000                                                                               040100 000                                                                               050206 001                                                                               060305 010                            010020 110 030102 000                                                                               040201 001                                                                               050200 001                                                                               060306 010                            010030 111 030103 000                                                                               040202 001                                                                               050301 010                                                                               060300 010                            010040 111 030104 000                                                                               040203 001                                                                               050302 010                                                                               060401 011                            010050 111 030105 000                                                                               040204 001                                                                               050303 010                                                                               060402 011                            010060 111 030106 000                                                                               040205 001                                                                               050304 010                                                                               060403 011                            020101 000 030100 000                                                                               040206 001                                                                               050305 010                                                                               060404 011                            020102 000 030201 001                                                                               040200 001                                                                               050306 010                                                                               060405 011                            020103 000 030202 001                                                                               040301 010                                                                               050300 010                                                                               060406 011                            020104 000 030203 001                                                                               040302 010                                                                               050401 011                                                                               060400 011                            020105 000 030204 001                                                                               040303 010                                                                               050402 011                                                                               060501 100                            020106 000 030205 001                                                                               040304 010                                                                               050403 011                                                                               060502 100                            060503 100 002001 110                                                                               200204 001                                                                               205001 100                                                                               302002 110                            060504 100 002002 110                                                                               200205 001                                                                               205002 100                                                                               302003 110                            060505 100 002003 110                                                                               200206 001                                                                               205003 100                                                                               302004 110                            060506 100 002004 110                                                                               200200 001                                                                               205004 100                                                                               302005 110                            060500 100 002005 110                                                                               200301 010                                                                               205005 100                                                                               302006 110                            060601 101 002006 110                                                                               200302 010                                                                               205006 100                                                                               302020 110                            060602 101 002020 110                                                                               200303 010                                                                               205020 100                                                                               302030 111                            060603 101 002030 111                                                                               200304 010                                                                               205030 101                                                                               302040 111                            060604 101 002040 111                                                                               200305 010                                                                               205040 101                                                                               302050 111                            060605 101 002050 111                                                                               200306 010                                                                               205050 101                                                                               302060 111                            060606 101 002060 111                                                                               200300 010                                                                               205060 101                                                                               303001 000                            060600 101 003001 000                                                                               200401 011                                                                               206001 110                                                                               303002 000                            060001 110 003002 000                                                                               200402 011                                                                               206002 110                                                                               303003 000                            060002 110 003003 000                                                                               200403 011                                                                               206003 110                                                                               303004 000                            060003 110 003004 000                                                                               200404 011                                                                               206004 110                                                                               303005 000                            060004 110 003005 000                                                                               200405 011                                                                               206005 110                                                                               303006 000                            060005 110 003006 000                                                                               200406 011                                                                               206006 110                                                                               303020 000                            060006 110 003020 000                                                                               200400 011                                                                               206020 110                                                                               303030 001                            060020 110 003030 001                                                                               200501 100                                                                               206030 111                                                                               303040 001                            060030 111 003040 001                                                                               200502 100                                                                               206040 111                                                                               303050 001                            060040 111 003050 001                                                                               200503 100                                                                               206050 111                                                                               303060 001                            060050 111 003060 001                                                                               200504 100                                                                               206060 111                                                                               304001 010                            060060 111 004001 010                                                                               200505 100                                                                               300101 000                                                                               304002 010                            000101 000 004002 010                                                                               200506 100                                                                               300102 000                                                                               304003 010                            000102 000 004003 010                                                                               200500 100                                                                               300103 000                                                                               304004 010                            000103 000 004004 010                                                                               200601 101                                                                               300104 000                                                                               304005 010                            000104 000 004005 010                                                                               200602 101                                                                               300105 000                                                                               304006 010                            000105 000 004006 010                                                                               200603 101                                                                               300106 000                                                                               304020 010                            000106 000 004020 010                                                                               200604 101                                                                               300100 000                                                                               304030 011                            000100 000 004030 011                                                                               200605 101                                                                               300201 001                                                                               304040 011                            000201 001 004040 011                                                                               200606 101                                                                               300202 001                                                                               304050 011                            000202 001 004050 011                                                                               200600 101                                                                               300203 001                                                                               304060 011                            000203 001 004060 011                                                                               202001 110                                                                               300204 001                                                                               305001 100                            000204 001 005001 100                                                                               202002 110                                                                               300205 001                                                                               305002 100                            000205 001 005002 100                                                                               202003 110                                                                               300206 001                                                                               305003 100                            000206 001 005003 100                                                                               202004 110                                                                               300200 001                                                                               305004 100                            000200 001 005004 100                                                                               202005 110                                                                               300301 010                                                                               305005 100                            000301 010 005005 100                                                                               202006 110                                                                               300302 010                                                                               305006 100                            000302 010 005006 100                                                                               202020 110                                                                               300303 010                                                                               305020 100                            000303 010 005020 100                                                                               202030 111                                                                               300304 010                                                                               305030 101                            000304 010 005030 101                                                                               202040 111                                                                               300305 010                                                                               305040 101                            000305 010 005040 101                                                                               202050 111                                                                               300306 010                                                                               305050 101                            000306 010 005050 101                                                                               202060 111                                                                               300300 010                                                                               305060 101                            000300 010 005060 101                                                                               203001 000                                                                               300401 011                                                                               306001 110                            000401 011 006001 110                                                                               203002 000                                                                               300402 011                                                                               306002 110                            000402 011 006002 110                                                                               203003 000                                                                               300403 011                                                                               306003 110                            000403 011 006003 110                                                                               203004 000                                                                               300404 011                                                                               306004 110                            000404 011 006004 110                                                                               203005 000                                                                               300405 011                                                                               306005 110                            000405 011 006005 110                                                                               203006 000                                                                               300406 011                                                                               306006 110                            000406 011 006006 110                                                                               203020 000                                                                               300400 011                                                                               306020 110                            000400 011 006020 110                                                                               203030 001                                                                               300501 100                                                                               306030 111                            000501 100 006030 111                                                                               203040 001                                                                               300502 100                                                                               306040 111                            000502 100 006040 111                                                                               203050 001                                                                               300503 100                                                                               306050 111                            000503 100 006050 111                                                                               203060 001                                                                               300504 100                                                                               306060 111                            000504 100 006060 111                                                                               204001 010                                                                               300505 100                                                                               400101 000                            000505 100 200101 000                                                                               204002 010                                                                               300506 100                                                                               400102 000                            000506 100 200102 000                                                                               204003 010                                                                               300500 100                                                                               400103 000                            000500 100 200103 000                                                                               204004 010                                                                               300601 101                                                                               400104 000                            000601 101 200104 000                                                                               204005 010                                                                               300602 101                                                                               400105 000                            000602 101 200105 000                                                                               204006 010                                                                               300603 101                                                                               400106 000                            000603 101 200106 000                                                                               204020 010                                                                               300604 101                                                                               400100 000                            000604 101 200100 000                                                                               204030 011                                                                               300605 101                                                                               400201 001                            000605 101 200201 001                                                                               204040 011                                                                               300606 101                                                                               400202 001                            000606 101 200202 001                                                                               204050 011                                                                               300600 101                                                                               400203 001                            000600 101 200203 001                                                                               204060 011                                                                               302001 110                                                                               400204 001                            400205 001 404004 010                                                                               500406 011                                                                               505030 101                                                                               600600 101                            400206 001 404005 010                                                                               500400 011                                                                               505040 101                                                                               602001 110                            400200 001 404006 010                                                                               500501 100                                                                               505050 101                                                                               602002 110                            400301 010 404020 010                                                                               500502 100                                                                               505060 101                                                                               602003 110                            400302 010 404030 011                                                                               500503 100                                                                               506001 110                                                                               602004 110                            400303 010 404040 011                                                                               500504 100                                                                               506002 110                                                                               602005 110                            400304 010 404050 011                                                                               500505 100                                                                               506003 110                                                                               602006 110                            400305 010 404060 011                                                                               500506 100                                                                               506004 110                                                                               602020 110                            400306 010 405001 100                                                                               500500 100                                                                               506005 110                                                                               602030 111                            400300 010 405002 100                                                                               500601 101                                                                               506006 110                                                                               602040 111                            400401 011 405003 100                                                                               500602 101                                                                               506020 110                                                                               602050 111                            400402 011 405004 100                                                                               500603 101                                                                               506030 111                                                                               602060 111                            400403 011 405005 100                                                                               500604 101                                                                               506040 111                                                                               603001 000                            400404 011 405006 100                                                                               500605 101                                                                               506050 111                                                                               603002 000                            400405 011 405020 100                                                                               500606 101                                                                               506060 111                                                                               603003 000                            400406 011 405030 101                                                                               500600 101                                                                               600101 000                                                                               603004 000                            400400 011 405040 101                                                                               502001 110                                                                               600102 000                                                                               603005 000                            400501 100 405050 101                                                                               502002 110                                                                               600103 000                                                                               603006 000                            400502 100 405060 101                                                                               502003 110                                                                               600104 000                                                                               603020 000                            400503 100 406001 110                                                                               502004 110                                                                               600105 000                                                                               603030 001                            400504 100 406002 110                                                                               502005 110                                                                               600106 000                                                                               603040 001                            400505 100 406003 110                                                                               502006 110                                                                               600100 000                                                                               603050 001                            400506 100 406004 110                                                                               502020 110                                                                               600201 001                                                                               603060 001                            400500 100 406005 110                                                                               502030 111                                                                               600202 001                                                                               604001 010                            400601 101 406006 110                                                                               502040 111                                                                               600203 001                                                                               604002 010                            400602 101 406020 110                                                                               502050 111                                                                               600204 001                                                                               604003 010                            400603 101 406030 111                                                                               502060 111                                                                               600205 001                                                                               604004 010                            400604 101 406040 111                                                                               503001 000                                                                               600206 001                                                                               604005 010                            400605 101 406050 111                                                                               503002 000                                                                               600200 001                                                                               604006 010                            400606 101 406060 111                                                                               503003 000                                                                               600301 010                                                                               604020 010                            400600 101 500101 000                                                                               503004 000                                                                               600302 010                                                                               604030 011                            402001 110 500102 000                                                                               503005 000                                                                               600303 010                                                                               604040 011                            402002 110 500103 000                                                                               503006 000                                                                               600304 010                                                                               604050 011                            402003 110 500104 000                                                                               503020 000                                                                               600305 010                                                                               604060 011                            402004 110 500105 000                                                                               503030 001                                                                               600306 010                                                                               605001 100                            402005 110 500106 000                                                                               503040 001                                                                               600300 010                                                                               605002 100                            402006 110 500100 000                                                                               503050 001                                                                               600401 011                                                                               605003 100                            402020 110 500201 001                                                                               503060 001                                                                               600402 011                                                                               605004 100                            402030 111 500202 001                                                                               504001 010                                                                               600403 011                                                                               605005 100                            402040 111 500203 001                                                                               504002 010                                                                               600404 011                                                                               605006 100                            402050 111 500204 001                                                                               504003 010                                                                               600405 011                                                                               605020 100                            402060 111 500205 001                                                                               504004 010                                                                               600406 011                                                                               605030 101                            403001 000 500206 001                                                                               504005 010                                                                               600400 011                                                                               605040 101                            403002 000 500200 001                                                                               504006 010                                                                               600501 100                                                                               605050 101                            403003 000 500301 010                                                                               504020 010                                                                               600502 100                                                                               605060 101                            403004 000 500302 010                                                                               504030 011                                                                               600503 100                                                                               606001 110                            403005 000 500303 010                                                                               504040 011                                                                               600504 100                                                                               606002 110                            403006 000 500304 010                                                                               304050 011                                                                               600505 100                                                                               606003 110                            403020 000 500305 010                                                                               504060 011                                                                               600506 100                                                                               606004 110                            403030 001 500306 010                                                                               505001 100                                                                               600500 100                                                                               606005 110                            403040 001 500300 010                                                                               505002 100                                                                               600601 101                                                                               606006 110                            403050 001 500401 011                                                                               505003 100                                                                               600602 101                                                                               606020 110                            403060 001 500402 011                                                                               505004 100                                                                               600603 101                                                                               606030 111                            404001 010 500403 011                                                                               505005 100                                                                               600604 101                                                                               606040 111                            404002 010 500404 011                                                                               505006 100                                                                               600605 101                                                                               606050 111                            404003 010 500405 011                                                                               505020 100                                                                               600606 101                                                                               606060 111                            __________________________________________________________________________

7. Conclusion

While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents. 

What is claimed is:
 1. A method for encoding a series of binary input data bits x into an M=7 run-length limited (1,3) code having a rate R=3/2, to produce a series of code symbols y, the method comprising the steps of receiving at a three-state encoder an input data bit set x_(i) . . . x_(i+2) to be encoded into the M=7 run-length limited (1,3) code, and generating in said encoder a code symbol set y_(i), y_(i+1) based on said input data bit set x_(i) . . . x_(i+2) according to the following mapping table:

    ______________________________________                                         INPUT        OUTPUT   NEXT STATE                                               ______________________________________                                         STATE 0                                                                        000          01       0                                                        001          02       0                                                        010          03       0                                                        011          04       0                                                        100          05       0                                                        101          06       0                                                        110          00       1                                                        111          00       2                                                        ______________________________________                                         STATE 1                                                                        000          01       0                                                        001          02       0                                                        010          03       0                                                        011          04       0                                                        100          05       0                                                        101          06       0                                                        110          20       1                                                        111          20       2                                                        ______________________________________                                         STATE 2                                                                        000          30       1                                                        001          30       2                                                        010          40       1                                                        011          40       2                                                        100          50       1                                                        101          50       2                                                        110          60       1                                                        111          60       2                                                        ______________________________________                                    

wherein said code symbol set y_(i), y_(i+1) is generated based on the input data bit set x_(i) . . . x_(i+2) and the current state of said three-state encoder when said data bit set x_(i) . . . x_(i+2) is received.
 2. A method for encoding a series of binary input data bits x into an M-ary run-length limited (1,3) code having a rate R=3/2 to produce a series of code symbols y, each code symbol being at one of M levels, where M>2 and each pair of non-zero code symbols having a minimum of one and a maximum of three zeroes therebetween, the method comprising the steps of receiving at a three-state encoder an input data bit set x_(i) . . . x_(i+2) to be encoded into the M-ary run-length limited (1,3) code, and generating in said encoder a code symbol set y_(i), Y_(i+1) based on said input data bit set x_(i) . . . x_(i+2) according to the following mapping table:

    ______________________________________                                         INPUT         OUTPUT   NEXT STATE                                              ______________________________________                                         STATE 0                                                                        000           01       0                                                       001           02       0                                                       010           03       0                                                       011           04       0                                                       100           05       0                                                       101           06       0                                                       110           00       1                                                       111           00       2                                                       STATE 1                                                                        000           01       0                                                       001           02       0                                                       010           03       0                                                       011           04       0                                                       100           05       0                                                       101           06       0                                                       110           20       1                                                       111           20       2                                                       STATE 2                                                                        000           30       1                                                       001           30       2                                                       010           40       1                                                       011           40       2                                                       100           50       1                                                       101           50       2                                                       110           60       1                                                       111           60       2                                                       ______________________________________                                    

wherein said code symbol set Y_(i), Y_(i+1) is generated based on the input data bit set x_(i) . . . x_(i+2), and the current state of said three-state encoder when said data bit set x_(i) . . . x_(i+2) is received.
 3. A method for converting binary input data bits into a series of waveform amplitudes each amplitude being at one of M=7 levels, the method comprising the steps of:encoding the binary input data bits into an M=7 (1,3) code having a rate R=3/2 to produce a series of code symbols, each code symbol being at one of M levels, and each pair of non-zero code symbols having a minimum of one and a maximum of three zeroes therebetween, said encoding step comprising the step of generating a code symbol set y_(i), y_(i+1) for each input data bit set x_(i) . . . x_(i+2) according to the following mapping table:

    ______________________________________                                         INPUT         OUTPUT   NEXT STATE                                              ______________________________________                                         STATE 0                                                                        000           01       0                                                       001           02       0                                                       010           03       0                                                       011           04       0                                                       100           05       0                                                       101           06       0                                                       110           00       1                                                       111           00       2                                                       STATE 1                                                                        000           01       0                                                       001           02       0                                                       010           03       0                                                       011           04       0                                                       100           05       0                                                       101           06       0                                                       110           20       1                                                       111           20       2                                                       STATE 2                                                                        000           30       1                                                       001           30       2                                                       010           40       1                                                       011           40       2                                                       100           50       1                                                       101           50       2                                                       110           60       1                                                       111           60       2                                                       ______________________________________                                    

wherein said code symbol set y_(i), y_(i+1) is generated based on the input data bit set x_(i) . . . x_(i+2) and the current state of said three-state encoder when said data bit set x_(i) . . . x_(i+2) is received; and generating in a waveform encoder waveform signal amplitudes based on said code symbols, wherein each said waveform signal amplitude is generated by modulo seven addition of a current code symbol with a previous waveform signal amplitude.
 4. In a data storage system having storage media capable of storing data at multiple levels, a method for converting binary input data bits into a series of waveform amplitudes each amplitude being at one of M=7 levels and storing the waveform amplitudes on the storage medium, the method comprising the steps of:encoding the binary input data bits into an M=7 (1,3) code having a rate R=3/2 to produce a series of code symbols, each code symbol being at one of M levels, and each pair of non-zero code symbols having a minimum of one and a maximum of three zeroes therebetween, comprising the step of generating a code symbol set y_(i), y_(i+1) for each input data bit set x_(i) . . . x_(i+2) according to the following mapping table:

    ______________________________________                                         INPUT         OUTPUT   NEXT STATE                                              ______________________________________                                         STATE 0                                                                        000           01       0                                                       001           02       0                                                       010           03       0                                                       011           04       0                                                       100           05       0                                                       101           06       0                                                       110           00       1                                                       111           00       2                                                       STATE 1                                                                        000           01       0                                                       001           02       0                                                       010           03       0                                                       011           04       0                                                       100           05       0                                                       101           06       0                                                       110           20       1                                                       111           20       2                                                       STATE 2                                                                        000           30       1                                                       001           30       2                                                       010           40       1                                                       011           40       2                                                       100           50       1                                                       101           50       2                                                       110           60       1                                                       111           60       2                                                       ______________________________________                                    

wherein a code symbol set y_(i), y_(i+1) generated for an input data bit set x_(i) . . . x_(i+2) is based on the input data bit set x_(i) . . . x_(i+2), and the current state of said three-state encoder when said data bit set x_(i) . . . x_(i+2) is received; generating in a waveform encoder waveform signal amplitudes based on said code symbols, wherein each said waveform signal amplitude is generated by modulo seven addition of a current code symbol with a previous waveform signal amplitude; and modulating a write signal with said waveform signal amplitudes to write a series of features to the storage medium, each feature being at a level corresponding to a waveform signal amplitude.
 5. The method according to claim 4, wherein said waveform signal amplitudes modulate a write laser and wherein said modulated write laser writes features onto the storage medium.
 6. The method according to claim 4, further comprising the steps of:reading the storage medium to recover output waveform signal amplitudes; converting said output waveform signal amplitudes into output code symbols, wherein each output code symbol is at one of seven levels; and decoding said output code symbols to obtain output data bits, wherein said output data bits correspond to the digital input data.
 7. The method of claim 6, wherein said step of decoding comprises the steps of:identifying with a sliding window a sequence of code symbols that represents a given code symbol set; and in a table comprising a number of entries corresponding to a number of possible unique sequences of code symbols, each entry identified by one of said possible unique sequences of code symbols, and wherein each entry identifies an output data bit set that is a decoded data bit set for the code symbol set represented by the sequence of code symbols that identifies that entry, looking up with said identified sequence of code symbols the output data bit for said given code symbol.
 8. The method according to claim 7, wherein said lookup table provides an output bit set x' for each sequence of code symbols y' according to the following table:

    __________________________________________________________________________     Sequence of                                                                               Sequence of                                                                              Sequence of                                                                              Sequence of                                                                              Sequence of                           Code       Code      Code      Code      Code                                  Symbols                                                                               x'  Symbols                                                                               x' Symbols                                                                               x' Symbols                                                                               x' Symbols                                                                               x'                             __________________________________________________________________________     010101 000 020100 000                                                                               030206 001                                                                               040305 010                                                                               050404 011                            010102 000 020201 001                                                                               030200 001                                                                               040306 010                                                                               050405 011                            010103 000 020202 001                                                                               030301 010                                                                               040300 010                                                                               050406 011                            010104 000 020203 001                                                                               030302 010                                                                               040401 011                                                                               050400 011                            010105 000 020204 001                                                                               030303 010                                                                               040402 011                                                                               050501 100                            010106 000 020205 001                                                                               030304 010                                                                               040403 011                                                                               050502 100                            010100 000 020206 001                                                                               030305 010                                                                               040404 011                                                                               050503 100                            010201 001 020200 001                                                                               030306 010                                                                               040405 011                                                                               050504 100                            010202 001 020301 010                                                                               030300 010                                                                               040406 011                                                                               050505 100                            010203 001 020302 010                                                                               030401 011                                                                               040400 011                                                                               050506 100                            010204 001 020303 010                                                                               030402 011                                                                               040501 100                                                                               050500 100                            010205 001 020304 010                                                                               030403 011                                                                               040502 100                                                                               050601 101                            010206 001 020305 010                                                                               030404 011                                                                               040503 100                                                                               050602 101                            010200 001 020306 010                                                                               030405 011                                                                               040504 100                                                                               050603 101                            010301 010 020300 010                                                                               030406 011                                                                               040505 100                                                                               050604 101                            010302 010 020401 011                                                                               030400 011                                                                               040506 100                                                                               050605 101                            010303 010 020402 011                                                                               030501 100                                                                               040500 100                                                                               050606 101                            010304 010 020403 011                                                                               030502 100                                                                               040601 101                                                                               050600 101                            010305 010 020404 011                                                                               030503 100                                                                               040602 101                                                                               050001 110                            010306 010 020405 011                                                                               030504 100                                                                               040603 101                                                                               050002 110                            010300 010 020406 011                                                                               030505 100                                                                               040604 101                                                                               050003 110                            010401 011 020400 011                                                                               030506 100                                                                               040605 101                                                                               050004 110                            010402 011 020501 100                                                                               030500 100                                                                               040606 101                                                                               050005 110                            010403 011 020502 100                                                                               030601 101                                                                               040600 101                                                                               050006 110                            010404 011 020503 100                                                                               030602 101                                                                               040001 110                                                                               050020 110                            010405 011 020504 100                                                                               030603 101                                                                               040002 110                                                                               050030 111                            010406 011 020505 100                                                                               030604 101                                                                               040003 110                                                                               050040 111                            010400 011 020506 100                                                                               030605 101                                                                               040004 110                                                                               050050 111                            010501 100 020500 100                                                                               030606 101                                                                               040005 110                                                                               050060 111                            010502 100 020601 101                                                                               030600 101                                                                               040006 110                                                                               060101 000                            010503 100 020602 101                                                                               030001 110                                                                               040020 110                                                                               060102 000                            010504 100 020603 101                                                                               030002 110                                                                               040030 111                                                                               060103 000                            010505 100 020604 101                                                                               030003 110                                                                               040040 111                                                                               060104 000                            010506 100 020605 101                                                                               030004 110                                                                               040050 111                                                                               060105 000                            010500 100 020606 101                                                                               030005 110                                                                               040060 111                                                                               060106 000                            010601 101 020600 101                                                                               030006 110                                                                               050101 000                                                                               060100 000                            010602 101 020001 110                                                                               030020 110                                                                               050102 000                                                                               060201 001                            010603 101 020002 110                                                                               030030 111                                                                               050103 000                                                                               060202 001                            010604 101 020003 110                                                                               030040 111                                                                               050104 000                                                                               060203 001                            010605 101 020004 110                                                                               030050 111                                                                               050105 000                                                                               060204 001                            010606 101 020005 110                                                                               030060 111                                                                               050106 000                                                                               060205 001                            010600 101 020006 110                                                                               040101 000                                                                               050100 000                                                                               060206 001                            010001 110 020020 110                                                                               040102 000                                                                               050201 001                                                                               060200 001                            010002 110 020030 111                                                                               040103 000                                                                               050202 001                                                                               060301 010                            010003 110 020040 111                                                                               040104 000                                                                               050203 001                                                                               060302 010                            010004 110 020050 111                                                                               040105 000                                                                               050204 001                                                                               060303 010                            010005 110 020060 111                                                                               040106 000                                                                               050205 001                                                                               060304 010                            010006 110 030101 000                                                                               040100 000                                                                               050206 001                                                                               060305 010                            010020 110 030102 000                                                                               040201 001                                                                               050200 001                                                                               060306 010                            010030 111 030103 000                                                                               040202 001                                                                               050301 010                                                                               060300 010                            010040 111 030104 000                                                                               040203 001                                                                               050302 010                                                                               060401 011                            010050 111 030105 000                                                                               040204 001                                                                               050303 010                                                                               060402 011                            010060 111 030106 000                                                                               040205 001                                                                               050304 010                                                                               060403 011                            020101 000 030100 000                                                                               040206 001                                                                               050305 010                                                                               060404 011                            020102 000 030201 001                                                                               040200 001                                                                               050306 010                                                                               060405 011                            020103 000 030202 001                                                                               040301 010                                                                               050300 010                                                                               060406 011                            020104 000 030203 001                                                                               040302 010                                                                               050401 011                                                                               060400 011                            020105 000 030204 001                                                                               040303 010                                                                               050402 011                                                                               060501 100                            020106 000 030205 001                                                                               040304 010                                                                               050403 011                                                                               060502 100                            060503 100 002001 110                                                                               200204 001                                                                               205001 100                                                                               302002 110                            060504 100 002002 110                                                                               200205 001                                                                               205002 100                                                                               302003 110                            060505 100 002003 110                                                                               200206 001                                                                               205003 100                                                                               302004 110                            060506 100 002004 110                                                                               200200 001                                                                               205004 100                                                                               302005 110                            060500 100 002005 110                                                                               200301 010                                                                               205005 100                                                                               302006 110                            060601 101 002006 110                                                                               200302 010                                                                               205006 100                                                                               302020 110                            060602 101 002020 110                                                                               200303 010                                                                               205020 100                                                                               302030 111                            060603 101 002030 111                                                                               200304 010                                                                               205030 101                                                                               302040 111                            060604 101 002040 111                                                                               200305 010                                                                               205040 101                                                                               302050 111                            060605 101 002050 111                                                                               200306 010                                                                               205050 101                                                                               302060 111                            060606 101 002060 111                                                                               200300 010                                                                               205060 101                                                                               303001 000                            060600 101 003001 000                                                                               200401 011                                                                               206001 110                                                                               303002 000                            060001 110 003002 000                                                                               200402 011                                                                               206002 110                                                                               303003 000                            060002 110 003003 000                                                                               200403 011                                                                               206003 110                                                                               303004 000                            060003 110 003004 000                                                                               200404 011                                                                               206004 110                                                                               303005 000                            060004 110 003005 000                                                                               200405 011                                                                               206005 110                                                                               303006 000                            060005 110 003006 000                                                                               200406 011                                                                               206006 110                                                                               303020 000                            060006 110 003020 000                                                                               200400 011                                                                               206020 110                                                                               303030 001                            060020 110 003030 001                                                                               200501 100                                                                               206030 111                                                                               303040 001                            060030 111 003040 001                                                                               200502 100                                                                               206040 111                                                                               303050 001                            060040 111 003050 001                                                                               200503 100                                                                               206050 111                                                                               303060 001                            060050 111 003060 001                                                                               200504 100                                                                               206060 111                                                                               304001 010                            060060 111 004001 010                                                                               200505 100                                                                               300101 000                                                                               304002 010                            000101 000 004002 010                                                                               200506 100                                                                               300102 000                                                                               304003 010                            000102 000 004003 010                                                                               200500 100                                                                               300103 000                                                                               304004 010                            000103 000 004004 010                                                                               200601 101                                                                               300104 000                                                                               304005 010                            000104 000 004005 010                                                                               200602 101                                                                               300105 000                                                                               304006 010                            000105 000 004006 010                                                                               200603 101                                                                               300106 000                                                                               304020 010                            000106 000 004020 010                                                                               200604 101                                                                               300100 000                                                                               304030 011                            000100 000 004030 011                                                                               200605 101                                                                               300201 001                                                                               304040 011                            000201 001 004040 011                                                                               200606 101                                                                               300202 001                                                                               304050 011                            000202 001 004050 011                                                                               200600 101                                                                               300203 001                                                                               304060 011                            000203 001 004060 011                                                                               202001 110                                                                               300204 001                                                                               305001 100                            000204 001 005001 100                                                                               202002 110                                                                               300205 001                                                                               305002 100                            000205 001 005002 100                                                                               202003 110                                                                               300206 001                                                                               305003 100                            000206 001 005003 100                                                                               202004 110                                                                               300200 001                                                                               305004 100                            000200 001 005004 100                                                                               202005 110                                                                               300301 010                                                                               305005 100                            000301 010 005005 100                                                                               202006 110                                                                               300302 010                                                                               305006 100                            000302 010 005006 100                                                                               202020 110                                                                               300303 010                                                                               305020 100                            000303 010 005020 100                                                                               202030 111                                                                               300304 010                                                                               305030 101                            000304 010 005030 101                                                                               202040 111                                                                               300305 010                                                                               305040 101                            000305 010 005040 101                                                                               202050 111                                                                               300306 010                                                                               305050 101                            000306 010 005050 101                                                                               202060 111                                                                               300300 010                                                                               305060 101                            000300 010 005060 101                                                                               203001 000                                                                               300401 011                                                                               306001 110                            000401 011 006001 110                                                                               203002 000                                                                               300402 011                                                                               306002 110                            000402 011 006002 110                                                                               203003 000                                                                               300403 011                                                                               306003 110                            000403 011 006003 110                                                                               203004 000                                                                               300404 011                                                                               306004 110                            000404 011 006004 110                                                                               203005 000                                                                               300405 011                                                                               306005 110                            000405 011 006005 110                                                                               203006 000                                                                               300406 011                                                                               306006 110                            000406 011 006006 110                                                                               203020 000                                                                               300400 011                                                                               306020 110                            000400 011 006020 110                                                                               203030 001                                                                               300501 100                                                                               306030 111                            000501 100 006030 111                                                                               203040 001                                                                               300502 100                                                                               306040 111                            000502 100 006040 111                                                                               203050 001                                                                               300503 100                                                                               306050 111                            000503 100 006050 111                                                                               203060 001                                                                               300504 100                                                                               306060 111                            000504 100 006060 111                                                                               204001 010                                                                               300505 100                                                                               400101 000                            000505 100 200101 000                                                                               204002 010                                                                               300506 100                                                                               400102 000                            000506 100 200102 000                                                                               204003 010                                                                               300500 100                                                                               400103 000                            000500 100 200103 000                                                                               204004 010                                                                               300601 101                                                                               400104 000                            000601 101 200104 000                                                                               204005 010                                                                               300602 101                                                                               400105 000                            000602 101 200105 000                                                                               204006 010                                                                               300603 101                                                                               400106 000                            000603 101 200106 000                                                                               204020 010                                                                               300604 101                                                                               400100 000                            000604 101 200100 000                                                                               204030 011                                                                               300605 101                                                                               400201 001                            000605 101 200201 001                                                                               204040 011                                                                               300606 101                                                                               400202 001                            000606 101 200202 001                                                                               204050 011                                                                               300600 101                                                                               400203 001                            000600 101 200203 001                                                                               204060 011                                                                               302001 110                                                                               400204 001                            400205 001 404004 010                                                                               500406 011                                                                               505030 101                                                                               600600 101                            400206 001 404005 010                                                                               500400 011                                                                               505040 101                                                                               602001 110                            400200 001 404006 010                                                                               500501 100                                                                               505050 101                                                                               602002 110                            400301 010 404020 010                                                                               500502 100                                                                               505060 101                                                                               602003 110                            400302 010 404030 011                                                                               500503 100                                                                               506001 110                                                                               602004 110                            400303 010 404040 011                                                                               500504 100                                                                               506002 110                                                                               602005 110                            400304 010 404050 011                                                                               500505 100                                                                               506003 110                                                                               602006 110                            400305 010 404060 011                                                                               500506 100                                                                               506004 110                                                                               602020 110                            400306 010 405001 100                                                                               500500 100                                                                               506005 110                                                                               602030 111                            400300 010 405002 100                                                                               500601 101                                                                               506006 110                                                                               602040 111                            400401 011 405003 100                                                                               500602 101                                                                               506020 110                                                                               602050 111                            400402 011 405004 100                                                                               500603 101                                                                               506030 111                                                                               602060 111                            400403 011 405005 100                                                                               500604 101                                                                               506040 111                                                                               603001 000                            400404 011 405006 100                                                                               500605 101                                                                               506050 111                                                                               603002 000                            400405 011 405020 100                                                                               500606 101                                                                               506060 111                                                                               603003 000                            400406 011 405030 101                                                                               500600 101                                                                               600101 000                                                                               603004 000                            400400 011 405040 101                                                                               502001 110                                                                               600102 000                                                                               603005 000                            400501 100 405050 101                                                                               502002 110                                                                               600103 000                                                                               603006 000                            400502 100 405060 101                                                                               502003 110                                                                               600104 000                                                                               603020 000                            400503 100 406001 110                                                                               502004 110                                                                               600105 000                                                                               603030 001                            400504 100 406002 110                                                                               502005 110                                                                               600106 000                                                                               603040 001                            400505 100 406003 110                                                                               502006 110                                                                               600100 000                                                                               603050 001                            400506 100 406004 110                                                                               502020 110                                                                               600201 001                                                                               603060 001                            400500 100 406005 110                                                                               502030 111                                                                               600202 001                                                                               604001 010                            400601 101 406006 110                                                                               502040 111                                                                               600203 001                                                                               604002 010                            400602 101 406020 110                                                                               502050 111                                                                               600204 001                                                                               604003 010                            400603 101 406030 111                                                                               502060 111                                                                               600205 001                                                                               604004 010                            400604 101 406040 111                                                                               503001 000                                                                               600206 001                                                                               604005 010                            400605 101 406050 111                                                                               503002 000                                                                               600200 001                                                                               604006 010                            400606 101 406060 111                                                                               503003 000                                                                               600301 010                                                                               604020 010                            400600 101 500101 000                                                                               503004 000                                                                               600302 010                                                                               604030 011                            402001 110 500102 000                                                                               503005 000                                                                               600303 010                                                                               604040 011                            402002 110 500103 000                                                                               503006 000                                                                               600304 010                                                                               604050 011                            402003 110 500104 000                                                                               503020 000                                                                               600305 010                                                                               604060 011                            402004 110 500105 000                                                                               503030 001                                                                               600306 010                                                                               605001 100                            402005 110 500106 000                                                                               503040 001                                                                               600300 010                                                                               605002 100                            402006 110 500100 000                                                                               503050 001                                                                               600401 011                                                                               605003 100                            402020 110 500201 001                                                                               503060 001                                                                               600402 011                                                                               605004 100                            402030 111 500202 001                                                                               504001 010                                                                               600403 011                                                                               605005 100                            402040 111 500203 001                                                                               504002 010                                                                               600404 011                                                                               605006 100                            402050 111 500204 001                                                                               504003 010                                                                               600405 011                                                                               605020 100                            402060 111 500205 001                                                                               504004 010                                                                               600406 011                                                                               605030 101                            403001 000 500206 001                                                                               504005 010                                                                               600400 011                                                                               605040 101                            403002 000 500200 001                                                                               504006 010                                                                               600501 100                                                                               605050 101                            403003 000 500301 010                                                                               504020 010                                                                               600502 100                                                                               605060 101                            403004 000 500302 010                                                                               504030 011                                                                               600503 100                                                                               606001 110                            403005 000 500303 010                                                                               504040 011                                                                               600504 100                                                                               606002 110                            403006 000 500304 010                                                                               304050 011                                                                               600505 100                                                                               606003 110                            403020 000 500305 010                                                                               504060 011                                                                               600506 100                                                                               606004 110                            403030 001 500306 010                                                                               505001 100                                                                               600500 100                                                                               606005 110                            403040 001 500300 010                                                                               505002 100                                                                               600601 101                                                                               606006 110                            403050 001 500401 011                                                                               505003 100                                                                               600602 101                                                                               606020 110                            403060 001 500402 011                                                                               505004 100                                                                               600603 101                                                                               606030 111                            404001 010 500403 011                                                                               505005 100                                                                               600604 101                                                                               606040 111                            404002 010 500404 011                                                                               505006 100                                                                               600605 101                                                                               606050 111                            404003 010 500405 011                                                                               505020 100                                                                               600606 101                                                                               606060 111                            __________________________________________________________________________


9. The method of claim 7, wherein said look-up step comprises the step of determining, using a squared euclidean distance, which table entry is identified by a sequence of code symbols.
 10. A method for decoding data stored on a storage medium, wherein said stored data has been encoding using an M=7 (1,3) code, comprising the steps of:reading the storage medium to recover output waveform signal amplitudes; converting said output waveform signal amplitudes into output code symbols, wherein each output code symbol is at one of seven levels; and decoding said output code symbols to obtain output data bits, wherein said output data bits correspond to the digital input data.
 11. The method of claim 10, wherein said step of decoding comprises the steps of:identifying with a sliding window a sequence of code symbols that represents a given code symbol set; and in a table comprising a number of entries corresponding to a number of possible unique sequences of code symbols, each entry identified by one of said possible unique sequences of code symbols, and wherein each entry identifies an output data bit set that is a decoded data bit set for the code symbol set represented by the sequence of code symbols that identifies that entry, looking up with said identified sequence of code symbols the output data bit for said given code symbol.
 12. The method according to claim 11, wherein said table provides an output bit set x' for each sequence of code symbols y' according to the following table:

    __________________________________________________________________________     Sequence of                                                                               Sequence of                                                                              Sequence of                                                                              Sequence of                                                                              Sequence of                           Code       Code      Code      Code      Code                                  Symbols                                                                               x'  Symbols                                                                               x' Symbols                                                                               x' Symbols                                                                               x' Symbols                                                                               x'                             __________________________________________________________________________     010101 000 020100 000                                                                               030206 001                                                                               040305 010                                                                               050404 011                            010102 000 020201 001                                                                               030200 001                                                                               040306 010                                                                               050405 011                            010103 000 020202 001                                                                               030301 010                                                                               040300 010                                                                               050406 011                            010104 000 020203 001                                                                               030302 010                                                                               040401 011                                                                               050400 011                            010105 000 020204 001                                                                               030303 010                                                                               040402 011                                                                               050501 100                            010106 000 020205 001                                                                               030304 010                                                                               040403 011                                                                               050502 100                            010100 000 020206 001                                                                               030305 010                                                                               040404 011                                                                               050503 100                            010201 001 020200 001                                                                               030306 010                                                                               040405 011                                                                               050504 100                            010202 001 020301 010                                                                               030300 010                                                                               040406 011                                                                               050505 100                            010203 001 020302 010                                                                               030401 011                                                                               040400 011                                                                               050506 100                            010204 001 020303 010                                                                               030402 011                                                                               040501 100                                                                               050500 100                            010205 001 020304 010                                                                               030403 011                                                                               040502 100                                                                               050601 101                            010206 001 020305 010                                                                               030404 011                                                                               040503 100                                                                               050602 101                            010200 001 020306 010                                                                               030405 011                                                                               040504 100                                                                               050603 101                            010301 010 020300 010                                                                               030406 011                                                                               040505 100                                                                               050604 101                            010302 010 020401 011                                                                               030400 011                                                                               040506 100                                                                               050605 101                            010303 010 020402 011                                                                               030501 100                                                                               040500 100                                                                               050606 101                            010304 010 020403 011                                                                               030502 100                                                                               040601 101                                                                               050600 101                            010305 010 020404 011                                                                               030503 100                                                                               040602 101                                                                               050001 110                            010306 010 020405 011                                                                               030504 100                                                                               040603 101                                                                               050002 110                            010300 010 020406 011                                                                               030505 100                                                                               040604 101                                                                               050003 110                            010401 011 020400 011                                                                               030506 100                                                                               040605 101                                                                               050004 110                            010402 011 020501 100                                                                               030500 100                                                                               040606 101                                                                               050005 110                            010403 011 020502 100                                                                               030601 101                                                                               040600 101                                                                               050006 110                            010404 011 020503 100                                                                               030602 101                                                                               040001 110                                                                               050020 110                            010405 011 020504 100                                                                               030603 101                                                                               040002 110                                                                               050030 111                            010406 011 020505 100                                                                               030604 101                                                                               040003 110                                                                               050040 111                            010400 011 020506 100                                                                               030605 101                                                                               040004 110                                                                               050050 111                            010501 100 020500 100                                                                               030606 101                                                                               040005 110                                                                               050060 111                            010502 100 020601 101                                                                               030600 101                                                                               040006 110                                                                               060101 000                            010503 100 020602 101                                                                               030001 110                                                                               040020 110                                                                               060102 000                            010504 100 020603 101                                                                               030002 110                                                                               040030 111                                                                               060103 000                            010505 100 020604 101                                                                               030003 110                                                                               040040 111                                                                               060104 000                            010506 100 020605 101                                                                               030004 110                                                                               040050 111                                                                               060105 000                            010500 100 020606 101                                                                               030005 110                                                                               040060 111                                                                               060106 000                            010601 101 020600 101                                                                               030006 110                                                                               050101 000                                                                               060100 000                            010602 101 020001 110                                                                               030020 110                                                                               050102 000                                                                               060201 001                            010603 101 020002 110                                                                               030030 111                                                                               050103 000                                                                               060202 001                            010604 101 020003 110                                                                               030040 111                                                                               050104 000                                                                               060203 001                            010605 101 020004 110                                                                               030050 111                                                                               050105 000                                                                               060204 001                            010606 101 020005 110                                                                               030060 111                                                                               050106 000                                                                               060205 001                            010600 101 020006 110                                                                               040101 000                                                                               050100 000                                                                               060206 001                            010001 110 020020 110                                                                               040102 000                                                                               050201 001                                                                               060200 001                            010002 110 020030 111                                                                               040103 000                                                                               050202 001                                                                               060301 010                            010003 110 020040 111                                                                               040104 000                                                                               050203 001                                                                               060302 010                            010004 110 020050 111                                                                               040105 000                                                                               050204 001                                                                               060303 010                            010005 110 020060 111                                                                               040106 000                                                                               050205 001                                                                               060304 010                            010006 110 030101 000                                                                               040100 000                                                                               050206 001                                                                               060305 010                            010020 110 030102 000                                                                               040201 001                                                                               050200 001                                                                               060306 010                            010030 111 030103 000                                                                               040202 001                                                                               050301 010                                                                               060300 010                            010040 111 030104 000                                                                               040203 001                                                                               050302 010                                                                               060401 011                            010050 111 030105 000                                                                               040204 001                                                                               050303 010                                                                               060402 011                            010060 111 030106 000                                                                               040205 001                                                                               050304 010                                                                               060403 011                            020101 000 030100 000                                                                               040206 001                                                                               050305 010                                                                               060404 011                            020102 000 030201 001                                                                               040200 001                                                                               050306 010                                                                               060405 011                            020103 000 030202 001                                                                               040301 010                                                                               050300 010                                                                               060406 011                            020104 000 030203 001                                                                               040302 010                                                                               050401 011                                                                               060400 011                            020105 000 030204 001                                                                               040303 010                                                                               050402 011                                                                               060501 100                            020106 000 030205 001                                                                               040304 010                                                                               050403 011                                                                               060502 100                            060503 100 002001 110                                                                               200204 001                                                                               205001 100                                                                               302002 110                            060504 100 002002 110                                                                               200205 001                                                                               205002 100                                                                               302003 110                            060505 100 002003 110                                                                               200206 001                                                                               205003 100                                                                               302004 110                            060506 100 002004 110                                                                               200200 001                                                                               205004 100                                                                               302005 110                            060500 100 002005 110                                                                               200301 010                                                                               205005 100                                                                               302006 110                            060601 101 002006 110                                                                               200302 010                                                                               205006 100                                                                               302020 110                            060602 101 002020 110                                                                               200303 010                                                                               205020 100                                                                               302030 111                            060603 101 002030 111                                                                               200304 010                                                                               205030 101                                                                               302040 111                            060604 101 002040 111                                                                               200305 010                                                                               205040 101                                                                               302050 111                            060605 101 002050 111                                                                               200306 010                                                                               205050 101                                                                               302060 111                            060606 101 002060 111                                                                               200300 010                                                                               205060 101                                                                               303001 000                            060600 101 003001 000                                                                               200401 011                                                                               206001 110                                                                               303002 000                            060001 110 003002 000                                                                               200402 011                                                                               206002 110                                                                               303003 000                            060002 110 003003 000                                                                               200403 011                                                                               206003 110                                                                               303004 000                            060003 110 003004 000                                                                               200404 011                                                                               206004 110                                                                               303005 000                            060004 110 003005 000                                                                               200405 011                                                                               206005 110                                                                               303006 000                            060005 110 003006 000                                                                               200406 011                                                                               206006 110                                                                               303020 000                            060006 110 003020 000                                                                               200400 011                                                                               206020 110                                                                               303030 001                            060020 110 003030 001                                                                               200501 100                                                                               206030 111                                                                               303040 001                            060030 111 003040 001                                                                               200502 100                                                                               206040 111                                                                               303050 001                            060040 111 003050 001                                                                               200503 100                                                                               206050 111                                                                               303060 001                            060050 111 003060 001                                                                               200504 100                                                                               206060 111                                                                               304001 010                            060060 111 004001 010                                                                               200505 100                                                                               300101 000                                                                               304002 010                            000101 000 004002 010                                                                               200506 100                                                                               300102 000                                                                               304003 010                            000102 000 004003 010                                                                               200500 100                                                                               300103 000                                                                               304004 010                            000103 000 004004 010                                                                               200601 101                                                                               300104 000                                                                               304005 010                            000104 000 004005 010                                                                               200602 101                                                                               300105 000                                                                               304006 010                            000105 000 004006 010                                                                               200603 101                                                                               300106 000                                                                               304020 010                            000106 000 004020 010                                                                               200604 101                                                                               300100 000                                                                               304030 011                            000100 000 004030 011                                                                               200605 101                                                                               300201 001                                                                               304040 011                            000201 001 004040 011                                                                               200606 101                                                                               300202 001                                                                               304050 011                            000202 001 004050 011                                                                               200600 101                                                                               300203 001                                                                               304060 011                            000203 001 004060 011                                                                               202001 110                                                                               300204 001                                                                               305001 100                            000204 001 005001 100                                                                               202002 110                                                                               300205 001                                                                               305002 100                            000205 001 005002 100                                                                               202003 110                                                                               300206 001                                                                               305003 100                            000206 001 005003 100                                                                               202004 110                                                                               300200 001                                                                               305004 100                            000200 001 005004 100                                                                               202005 110                                                                               300301 010                                                                               305005 100                            000301 010 005005 100                                                                               202006 110                                                                               300302 010                                                                               305006 100                            000302 010 005006 100                                                                               202020 110                                                                               300303 010                                                                               305020 100                            000303 010 005020 100                                                                               202030 111                                                                               300304 010                                                                               305030 101                            000304 010 005030 101                                                                               202040 111                                                                               300305 010                                                                               305040 101                            000305 010 005040 101                                                                               202050 111                                                                               300306 010                                                                               305050 101                            000306 010 005050 101                                                                               202060 111                                                                               300300 010                                                                               305060 101                            000300 010 005060 101                                                                               203001 000                                                                               300401 011                                                                               306001 110                            000401 011 006001 110                                                                               203002 000                                                                               300402 011                                                                               306002 110                            000402 011 006002 110                                                                               203003 000                                                                               300403 011                                                                               306003 110                            000403 011 006003 110                                                                               203004 000                                                                               300404 011                                                                               306004 110                            000404 011 006004 110                                                                               203005 000                                                                               300405 011                                                                               306005 110                            000405 011 006005 110                                                                               203006 000                                                                               300406 011                                                                               306006 110                            000406 011 006006 110                                                                               203020 000                                                                               300400 011                                                                               306020 110                            000400 011 006020 110                                                                               203030 001                                                                               300501 100                                                                               306030 111                            000501 100 006030 111                                                                               203040 001                                                                               300502 100                                                                               306040 111                            000502 100 006040 111                                                                               203050 001                                                                               300503 100                                                                               306050 111                            000503 100 006050 111                                                                               203060 001                                                                               300504 100                                                                               306060 111                            000504 100 006060 111                                                                               204001 010                                                                               300505 100                                                                               400101 000                            000505 100 200101 000                                                                               204002 010                                                                               300506 100                                                                               400102 000                            000506 100 200102 000                                                                               204003 010                                                                               300500 100                                                                               400103 000                            000500 100 200103 000                                                                               204004 010                                                                               300601 101                                                                               400104 000                            000601 101 200104 000                                                                               204005 010                                                                               300602 101                                                                               400105 000                            000602 101 200105 000                                                                               204006 010                                                                               300603 101                                                                               400106 000                            000603 101 200106 000                                                                               204020 010                                                                               300604 101                                                                               400100 000                            000604 101 200100 000                                                                               204030 011                                                                               300605 101                                                                               400201 001                            000605 101 200201 001                                                                               204040 011                                                                               300606 101                                                                               400202 001                            000606 101 200202 001                                                                               204050 011                                                                               300600 101                                                                               400203 001                            000600 101 200203 001                                                                               204060 011                                                                               302001 110                                                                               400204 001                            400205 001 404004 010                                                                               500406 011                                                                               505030 101                                                                               600600 101                            400206 001 404005 010                                                                               500400 011                                                                               505040 101                                                                               602001 110                            400200 001 404006 010                                                                               500501 100                                                                               505050 101                                                                               602002 110                            400301 010 404020 010                                                                               500502 100                                                                               505060 101                                                                               602003 110                            400302 010 404030 011                                                                               500503 100                                                                               506001 110                                                                               602004 110                            400303 010 404040 011                                                                               500504 100                                                                               506002 110                                                                               602005 110                            400304 010 404050 011                                                                               500505 100                                                                               506003 110                                                                               602006 110                            400305 010 404060 011                                                                               500506 100                                                                               506004 110                                                                               602020 110                            400306 010 405001 100                                                                               500500 100                                                                               506005 110                                                                               602030 111                            400300 010 405002 100                                                                               500601 101                                                                               506006 110                                                                               602040 111                            400401 011 405003 100                                                                               500602 101                                                                               506020 110                                                                               602050 111                            400402 011 405004 100                                                                               500603 101                                                                               506030 111                                                                               602060 111                            400403 011 405005 100                                                                               500604 101                                                                               506040 111                                                                               603001 000                            400404 011 405006 100                                                                               500605 101                                                                               506050 111                                                                               603002 000                            400405 011 405020 100                                                                               500606 101                                                                               506060 111                                                                               603003 000                            400406 011 405030 101                                                                               500600 101                                                                               600101 000                                                                               603004 000                            400400 011 405040 101                                                                               502001 110                                                                               600102 000                                                                               603005 000                            400501 100 405050 101                                                                               502002 110                                                                               600103 000                                                                               603006 000                            400502 100 405060 101                                                                               502003 110                                                                               600104 000                                                                               603020 000                            400503 100 406001 110                                                                               502004 110                                                                               600105 000                                                                               603030 001                            400504 100 406002 110                                                                               502005 110                                                                               600106 000                                                                               603040 001                            400505 100 406003 110                                                                               502006 110                                                                               600100 000                                                                               603050 001                            400506 100 406004 110                                                                               502020 110                                                                               600201 001                                                                               603060 001                            400500 100 406005 110                                                                               502030 111                                                                               600202 001                                                                               604001 010                            400601 101 406006 110                                                                               502040 111                                                                               600203 001                                                                               604002 010                            400602 101 406020 110                                                                               502050 111                                                                               600204 001                                                                               604003 010                            400603 101 406030 111                                                                               502060 111                                                                               600205 001                                                                               604004 010                            400604 101 406040 111                                                                               503001 000                                                                               600206 001                                                                               604005 010                            400605 101 406050 111                                                                               503002 000                                                                               600200 001                                                                               604006 010                            400606 101 406060 111                                                                               503003 000                                                                               600301 010                                                                               604020 010                            400600 101 500101 000                                                                               503004 000                                                                               600302 010                                                                               604030 011                            402001 110 500102 000                                                                               503005 000                                                                               600303 010                                                                               604040 011                            402002 110 500103 000                                                                               503006 000                                                                               600304 010                                                                               604050 011                            402003 110 500104 000                                                                               503020 000                                                                               600305 010                                                                               604060 011                            402004 110 500105 000                                                                               503030 001                                                                               600306 010                                                                               605001 100                            402005 110 500106 000                                                                               503040 001                                                                               600300 010                                                                               605002 100                            402006 110 500100 000                                                                               503050 001                                                                               600401 011                                                                               605003 100                            402020 110 500201 001                                                                               503060 001                                                                               600402 011                                                                               605004 100                            402030 111 500202 001                                                                               504001 010                                                                               600403 011                                                                               605005 100                            402040 111 500203 001                                                                               504002 010                                                                               600404 011                                                                               605006 100                            402050 111 500204 001                                                                               504003 010                                                                               600405 011                                                                               605020 100                            402060 111 500205 001                                                                               504004 010                                                                               600406 011                                                                               605030 101                            403001 000 500206 001                                                                               504005 010                                                                               600400 011                                                                               605040 101                            403002 000 500200 001                                                                               504006 010                                                                               600501 100                                                                               605050 101                            403003 000 500301 010                                                                               504020 010                                                                               600502 100                                                                               605060 101                            403004 000 500302 010                                                                               504030 011                                                                               600503 100                                                                               606001 110                            403005 000 500303 010                                                                               504040 011                                                                               600504 100                                                                               606002 110                            403006 000 500304 010                                                                               304050 011                                                                               600505 100                                                                               606003 110                            403020 000 500305 010                                                                               504060 011                                                                               600506 100                                                                               606004 110                            403030 001 500306 010                                                                               505001 100                                                                               600500 100                                                                               606005 110                            403040 001 500300 010                                                                               505002 100                                                                               600601 101                                                                               606006 110                            403050 001 500401 011                                                                               505003 100                                                                               600602 101                                                                               606020 110                            403060 001 500402 011                                                                               505004 100                                                                               600603 101                                                                               606030 111                            404001 010 500403 011                                                                               505005 100                                                                               600604 101                                                                               606040 111                            404002 010 500404 011                                                                               505006 100                                                                               600605 101                                                                               606050 111                            404003 010 500405 011                                                                               505020 100                                                                               600606 101                                                                               606060 111                            __________________________________________________________________________ 